CN108880225A - A kind of non-linear modeling method of inverse-excitation type pfc converter - Google Patents
A kind of non-linear modeling method of inverse-excitation type pfc converter Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/42—Circuits or arrangements for compensating for or adjusting power factor in converters or inverters
- H02M1/4208—Arrangements for improving power factor of AC input
- H02M1/4258—Arrangements for improving power factor of AC input using a single converter stage both for correction of AC input power factor and generation of a regulated and galvanically isolated DC output voltage
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M1/00—Details of apparatus for conversion
- H02M1/0003—Details of control, feedback or regulation circuits
- H02M1/0012—Control circuits using digital or numerical techniques
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
- Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
- Y02B70/10—Technologies improving the efficiency by using switched-mode power supplies [SMPS], i.e. efficient power electronics conversion e.g. power factor correction or reduction of losses in power supplies or efficient standby modes
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Abstract
A kind of non-linear modeling method of inverse-excitation type pfc converter, Peak-current Controlled Flyback pfc converter is modeled using stroboscopic map method, based on this model, numerical simulation has been carried out to fast-scale wild effect, the result shows that, in fast-scale unstable region, not only there is bifurcation phenomena, goes back while having the generation of border collision bifurcation and chaos.Influence of the present invention by the value of primary study circuit parameter to mission nonlinear, the position occurred by the calculating concrete analysis bifurcation point of Jacobian matrix characteristic root and corresponding circuit parameter values, so that the design for inverse-excitation type pfc circuit provides certain theoretical foundation.
Description
Technical field
The present invention relates to inverse-excitation type pfc converter, especially a kind of non-linear modeling method of inverse-excitation type pfc converter,
Belong to switch power technology field.
Background technique
In recent years, widely using Flyback pfc converter as supression harmonic wave in high-power electric and electronic circuit
The effective means of pollution, for solving its harmonic pollution problems got worse to power grid.Since there are switch and multipliers
Equal nonlinear devices, Flyback pfc converter is substantially a kind of strongly non-linear system.Therefore, using nonlinear kinetics
The working characteristics of technique study pfc converter has become the current hot spot paid close attention in relation to academia and engineering circles, same to non-linear hour
The attention that the research of modeling has also obtained more and more.
While pfc converter modeling method is constantly broken through, the research of pfc converter non-linear phenomena is also by model
Development also achieve a series of achievement.2010, Orabi had studied what pfc converter occurred under different load conditions
Non-linear behavior gives the loading range under pfc converter steady operation, while having made a concrete analysis of caused by period doubling bifurcation
Subharmonic oscillation, this method are suitable only for the pfc converter of two-stage, for single- stage PFC circuit since input voltage is at one
Constantly change the non-linear behavior for causing this method that can not embody single- stage PFC circuit very well in period.2013, Tse was further
The reason of Switching Power Supply non-linear phenomena occurs is analyzed, gives influence of the different switching frequencies to mission nonlinear, still
Herein there is no switching frequency parameter and non-linear phenomena get in touch be further analyzed but primary study one kind
Non-linear inhibition method.2016, the A Gosh further in-depth study non-linear behavior of pfc converter had studied times
Periodic Bifurcation and chaos state, and using load capacitance as caused by fork parameter study different loads capacitor value range
The different non-linear phenomena of pfc converter.But the calculating of the bifurcation point parameter of this paper is still the side by computer graphics
Method can not provide accurate numerical value.
Summary of the invention
The technical solution adopted by the present invention is as follows：A kind of non-linear modeling method of inverse-excitation type pfc converter, feature exist
In：It establishes inverse excitation type converter master and opens up the state equation for mending structure, Discrete Mapping model, base are established by way of continuous sampling
In this Discrete Mapping model, the specific range of different nonlinear states is calculated using calculating Jacobian matrix, is included the following steps：
1) it establishes master and opens up benefit state equation
Power supply status equation when switching tube S1 is opened and turned off is listed respectively, while being considered then in entire switch periods
Interior, switching tube S1 is connected always to be first connected the two states turned off afterwards to switching tube S1 within the period and lists relevant state side
Journey,
When switching tube S1 conducting, the state equation of inverse-excitation type switch power-supply is：
Wherein iLMFor primary side inductive current, LmFor primary side inductance, Vin is input voltage, VCIt is load for output voltage, R
Resistance, C are load capacitance；
When switching tube S1 is disconnected, the state equation of inverse-excitation type switch power-supply is：
Formula (2) gives the state space equation of inverse excitation type converter, further sharp on the basis of this state space equation
The accurate model of system is provided with discrete hidden Markov models method, wherein N1 and N2 respectively represents the umber of turn of primary and secondary side；
2) sample states variable
Using the discrete iteration mapping model of stroboscopic map construction peak point current Flyback pfc converter, peak value is established
When the discrete iteration mapping model of the pfc converter of current control, need to sample state variable, if in=iL (nT),
Vn=vC (nT) is respectively the sampled value of inductive current and capacitance voltage at the nT moment, then in+1, vn+1 are respectively inductive current
Sampled value with capacitance voltage at (n+1) the T moment, wherein switching occurs as iL=Iref；
The turn-on time of switching tube is calculated first, it is assumed that loop uses Peak Current Mode control mode, then reference current is
Iref=K | sin (ω t) | (3)
Wherein K is corresponding proportionality coefficient, and ω is switching tube period 50kHz, and the line voltage period is 50Hz, therefore,
One switch periods internal reference examination point stream is equivalent to a fixed value：
Iref=K | sin (ω nT) | (4)
Wherein n indicates n-th of period of system starts, while the line voltage in a switch periods is also solid by one
Definite value replaces, and is
Vin=VM| sin ω t |=VM|sinωnT| (5)
Wherein VMFor input voltage amplitude, then by formula (3), formula (4) and formula (5) acquire the turn-on time of switching tube：
Finish time t is connected in switching tuben, have：
Wherein output voltage when n-th of end cycle of Vn expression, since converter uses the side of Peak Current Mode control
The current value that finish time inductance is connected in formula, i.e. switching tube is equal with reference voltage value, therefore inductive current i (tn)=Iref=K |
sin(ωt)| (8)
3) consider inverse excitation type converter working condition
According to the length for the time that switching tube is opened, the working condition of inverse excitation type converter is divided into following state, wherein T
Indicate switch periods；
Mode one：tn≥T
Then in entire switch periods, switching tube is connected always, then has
Mode two：tn<T solves formula (5), obtains formulation character root：
Wherein n=N2/N1；
Mode three：tn<T and system enter DCM operating mode, i.e., the electric current carved in end cycle in inductance has been 0
Then
By above-mentioned derivation, the n period is established to the voltage-current relationship between the n+1 period, it can by successive ignition
The state of circuit when enough calculating any end cycle has tentatively established the Discrete Mapping model of system to this；
4) Jacobian matrix and Bifurcation
Fixed point iQ, vQ are found out by in+1=in=iQ, vn+1=vn=vQ, this is a non-linear transcendental equation,
Numerical solution is found out by Newton-Raphson method or other iterative algorithms, in order to analyze the unstability situation at fixed point i.e. times week
Phase fork, needs to find out the Jacobian matrix of motionless vertex neighborhood, in practical applications, it is desirable to which inverse-excitation type pfc converter can be stablized
Work at this point, system only switches between mode one and mode two, and does not suffer from mode three, therefore only need in one state of period
The Jacobian matrix of mapping equation (12) is analyzed, Jacobian matrix such as formula (13) is obtained, which is
Obtained nonlinear model：
The characteristic equation of Jacobian matrix is represented by fixed point：
Det (λ I-J)=0 (14)
Wherein I indicates that unit vector, λ are the characteristic root of required solution.System fixed point i is acquired by recurrence formulaQ,vQ, by
This acquires the Jacobian matrix in fixed point field, and fixed point is determined by Nonlinear System of Equations (13), by resulting to formula (14)
The analysis of feature root locus, it will be able to determine the instability boundary of system；
5) Jacobian matrix obtained according to step 4 just realizes the Nonlinear Modeling process of inverse excitation type converter, passes through
Formula (14) can analyze the nonlinear state of circuit.
Advantages of the present invention and remarkable result：The present invention is using stroboscopic map method to Peak-current Controlled Flyback
Pfc converter is modeled, and a set of segmentation Smooth Maps equation has been obtained, and is based on this model, unstable to fast-scale existing
As having carried out numerical simulation, the results showed that, in fast-scale unstable region, not only there is bifurcation phenomena, it is also same
When have the generation of border collision bifurcation and chaos.Shadow of the value of primary study of the present invention circuit parameter to mission nonlinear
It rings, by the calculating of Jacobian matrix characteristic root, makes a concrete analysis of the position and corresponding circuit parameter values that bifurcation point occurs, from
And the design for inverse-excitation type pfc circuit provides theoretical foundation.
Detailed description of the invention
Fig. 1 is typical inverse-excitation type pfc circuit structure；
Fig. 2 is discrete iteration mapping model；
Fig. 3 is the waveform diagram of inductive current iLm after stable state；
Fig. 4 is voltage-phase 0<θ<θ1When inductance waveform；
Fig. 5 is voltage-phase θ1<θ<θ2When inductance waveform；
Fig. 6 is voltage-phase θ2<θ<The waveform of inductance when π；
Fig. 7 is the distribution map of switch conduction duty ratio in one cycle；
Fig. 8 is R=100 Ω inductive current waveform；
Fig. 9 is R=150 Ω inductive current waveform.
Specific embodiment
Fig. 1 gives the typical structure of inverse-excitation type pfc circuit, based on including that sequentially connected rectifier bridge, inverse-excitation type open up benefit
The control system that structure and control IC are constituted.Power factor characterizes system to the utilization efficiency of power grid, and wherein power factor is fixed
Justice is as follows, defines the ratio that power factor is active-power P and apparent energy S, i.e.,：
Wherein, URFor network voltage virtual value, IRFor input current virtual value, UIFor input voltage fundamental wave virtual value, IIFor
Input current fundamental wave virtual value,For displacement factor, the phase size between fundamental current and voltage has been reacted.So PFization
Letter is following formula：
Wherein, ξ has reacted the degree that current waveform deviates sine wave.The distortion of input current is so that rectifier input current
Rated value increases, and efficiency is caused to reduce.It can be obtained by formula (16), under conditions of current waveform distortion level is certain, when input electricity
When pressing equal with the phase of input current, the PF of system reaches maximum value.Therefore it assume that one for inverse-excitation type pfc circuit
Reference current：Iref=Ksin ω t (17)
Wherein K is a constant, using reference current shown in formula (17) as the peak value of input current, it is ensured that input electricity
The phase approximation and input current phase of the whole envelope of stream, therefore ensure that high PF.
Fig. 2 gives the establishment process of Discrete Mapping model, constructs peak point current Flyback converter using stroboscopic map
Discrete iteration mapping model, as shown in Fig. 2, setting in=iL(nT), vn=vCIt (nT) is respectively that inductive current and capacitance voltage exist
The sampled value at nT moment, then in+1, vn+1The respectively sampled value of inductive current and capacitance voltage at (n+1) the T moment, wherein working as iL
=IrefShi Fasheng switching.
Fig. 3 gives the waveform diagram that system enters inductive current iLm after stable state, as can be seen from the figure inductive current
It experienced three kinds of different conditions in a power frequency period, when input voltage phase is 0<θ<θ1When, inductive current is shown not
Stable phenomenon (period doubling bifurcation and chaos)；When input voltage phase is θ1<θ<θ2When, inductive current enters the stable period
One state；As input voltage phase θ2<θ<When π, inductive current is re-introduced into unstable state (period doubling bifurcation and chaos).
In the phenomenon and DC-DC converter, the bifurcation phenomena occurred when input voltage is too low is similar, but for inverse-excitation type
Input voltage is in cyclically-varying for pfc circuit, therefore the non-linear phenomena occurred also shows certain intermittence.As above
Analysis is stated, within every 1/2 input voltage period, system meeting intermittent (input voltage is too low) not inverse-excitation type pfc circuit occurs
Stabilization.
For the non-linear behavior for making a concrete analysis of inductive current in each period, the waveform of the inductive current of three states is put
Greatly, respectively as shown in Figure 4,5, 6, wherein Fig. 4 gives voltage-phase 0<θ<θ1When inductance waveform, Fig. 5 gives θ1<θ<θ2
When inductance waveform, Fig. 6 gives θ2<θ<Waveform when π.
As shown in fig. 7, the distribution map of switch conduction duty ratio in one cycle is given, it can be found that in above-mentioned analysis
θ1And θ2Place, duty ratio similarly enter period doubling bifurcation state.And at t=1, the duty ratio of switch conduction reaches 1.
It is above-mentioned analysis shows, in unstable region, circuit state frequent switching, existing doubling time between mode 1, mode 2 and mode 3
Accumulation also have the generation of border collision, it can be seen that have to the research of the non-linear behavior of inverse-excitation type pfc circuit very heavy
The theory significance wanted.
The waveform of inductive current, can obtain θ from figure when Fig. 8 gives load resistance R=100 Ω1=21.6 °, θ2=
156.8 °, stable phase range at this time is θ2-θ1=135.2 °.Changing load resistance makes resistance value R=100, electricity at this time
Inducing current waveform from figure as shown in figure 8, can obtain θ1=58, θ2=149, stable phase range at this time is：θ2-θ1=91.
Load resistor value R is further increased, the waveform of inductive current when Fig. 9 gives R=150 Ω can be obtained, system is entire by Fig. 9
It is all shown in switch periods non-linear.Analysis shows, with the increase of load resistance R, inverse-excitation type pfc circuit is at one above
Stability region in period constantly reduces.
Claims (1)
1. a kind of non-linear modeling method of inverse-excitation type pfc converter, it is characterised in that：It establishes inverse excitation type converter master and opens up benefit knot
The state equation of structure establishes Discrete Mapping model by way of continuous sampling, is based on this Discrete Mapping model, refined using calculating
The specific range that different nonlinear states gram are calculated than matrix, includes the following steps：
1) it establishes master and opens up benefit state equation
List respectively switching tube S1 open with power supply status equation when shutdown, while considering then in entire switch periods, open
It closes pipe S1 and is connected always and the two states turned off afterwards are first connected within the period to switching tube S1 list relevant state equation,
When switching tube S1 conducting, the state equation of inverse-excitation type switch power-supply is：
Wherein iLMFor primary side inductive current, LmFor primary side inductance, Vin is input voltage, VCIt is load resistance, C for output voltage, R
For load capacitance；
When switching tube S1 is disconnected, the state equation of inverse-excitation type switch power-supply is：
Formula (2) gives the state space equation of inverse excitation type converter, on the basis of this state space equation, further utilize from
The accurate model that mapping, modeling method provides system is dissipated, wherein N1 and N2 respectively represents the umber of turn of primary and secondary side；
2) sample states variable
Using the discrete iteration mapping model of stroboscopic map construction peak point current Flyback pfc converter, peak point current is established
It when the discrete iteration mapping model of the pfc converter of control, needs to sample state variable, if in=iL (nT), vn=
VC (nT) is respectively the sampled value of inductive current and capacitance voltage at the nT moment, then in+1, vn+1 are respectively inductive current and electricity
Hold sampled value of the voltage at (n+1) the T moment, wherein switching occurs as iL=Iref；
The turn-on time of switching tube is calculated first, it is assumed that loop uses Peak Current Mode control mode, then reference current is
Iref=K | sin (ω t) | (3)
Wherein K is corresponding proportionality coefficient, and ω is switching tube period 50kHz, and the line voltage period is 50Hz, therefore, at one
Switch periods internal reference examination point stream is equivalent to a fixed value：
Iref=K | sin (ω nT) | (4)
Wherein n indicates n-th of period of system starts, while the line voltage in a switch periods is also by a fixed value
Instead of being
Vin=VM| sin ω t |=VM|sinωnT| (5)
Wherein VMFor input voltage amplitude, then by formula (3), formula (4) and formula (5) acquire the turn-on time of switching tube：
Finish time t is connected in switching tuben, have：
Wherein output voltage when n-th of end cycle of Vn expression, since converter is by the way of Peak Current Mode control, i.e.,
The current value that finish time inductance is connected in switching tube is equal with reference voltage value, therefore inductive current i (tn)=Iref=K | sin (ω
t)| (8)
3) consider inverse excitation type converter working condition
According to the length for the time that switching tube is opened, the working condition of inverse excitation type converter is divided into following state, wherein T is indicated
Switch periods；
Mode one：tn≥T
Then in entire switch periods, switching tube is connected always, then has
Mode two：tn<T solves formula (5), obtains formulation character root：
Wherein n=N2/N1；
Mode three：tn<T and system enter DCM operating mode, i.e., the electric current carved in end cycle in inductance has been 0, then
By above-mentioned derivation, the n period is established to the voltage-current relationship between the n+1 period, can be counted by successive ignition
The state of circuit when calculating any end cycle has tentatively established the Discrete Mapping model of system to this；
4) Jacobian matrix and Bifurcation
Fixed point iQ, vQ are found out by in+1=in=iQ, vn+1=vn=vQ, this is a non-linear transcendental equation, numerical value
Solution is found out by Newton-Raphson method or other iterative algorithms, in order to analyze the unstability situation i.e. doubling time point at fixed point
Trouble, needs to find out the Jacobian matrix of motionless vertex neighborhood, in practical applications, it is desirable to inverse-excitation type pfc converter energy steady operation
In one state of period, at this point, system only switches between mode one and mode two, and mode three is not suffered from, therefore only need mapping
The Jacobian matrix for penetrating equation (12) is analyzed, and Jacobian matrix such as formula (13) is obtained, which is required
The nonlinear model obtained：
The characteristic equation of Jacobian matrix is represented by fixed point：
Det (λ I-J)=0 (14)
Wherein I indicates that unit vector, λ are the characteristic root of required solution；System fixed point i is acquired by recurrence formulaQ,vQ, thus ask
The Jacobian matrix in fixed point field is obtained, fixed point is determined by Nonlinear System of Equations (13), by formula (14) resulting feature
The analysis of root locus, it will be able to determine the instability boundary of system；
5) Jacobian matrix obtained according to step 4 just realizes the Nonlinear Modeling process of inverse excitation type converter, passes through formula
(14) nonlinear state of circuit can be analyzed.
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